GlobSol user guide

Abstract

We explain the installation and use of the GlobSol package for mathematically rigorous bounds on all solutions to constrained and unconstrained global optimization problems, as well as non-linear systems of equations. This document should be of use both to people with optimization problems to solve and to people incorporating GlobSol's components into other systems or providing interfaces to GlobSol.

Keywords:

• nonconvex optimization
• global optimization
• GlobSol
• constraint propagation

AMS Subject Classification :

• 90C30
• 65K05
• 90C26
• 65G20

Acknowledgements

The author thanks others who have worked on GlobSol and have made it possible. In particular, he thanks his former students, the authors of 12, who also worked on early versions of GlobSol. He thanks Bill Walster and SunSoft for support during development and George Corliss for testing, use of early versions, contributions of some of the modules and scripts, and much advice on software development. The author also thanks Arnold Neumaier and the Erwin Schrödinger Institute for support while in Vienna in December 2006.

Notes

This forces the GlobSol algorithms to differ in various important respects from algorithms that do not claim to provide solutions with mathematical rigour; see, for example, 8.

It can be assured that GlobSol-win-gnu.correct_IO.exe is run from ⟨GlobSol root dir> by running it from a command prompt in that directory.

Included in this GlobSol distribution, and often included in Linux distributions.

So it will execute with many versions of ‘make.’

The main difference between these two versions is the use of ‘\’ in path names instead of ‘/’, and care must be taken in converting between the two.

This script is meant for Sun Solaris with the Sun Fortran compiler. However, the script is largely generic.

A copy of this script, named ‘globsol.bat’ on Windows systems and ‘globsol’ on Unix or Linux systems, resides on <GlobSol root dir>.

However, portions or elements of the array can be passed as arguments to a subroutine, in which the individual arguments are given different names.

The name stands for ‘code list left-hand side.’

The box data file may have a file type DT?, where ‘?’ can be any digit between 0 and 9. This digit is passed to the globsol script to control which of possibly several box data files is used.

In the present version of GlobSol.

About in IEEE standard arithmetic.

n lines for n independent variables.

If there are n independent variables, then there will be n such lines.

Because this method may result in better upper bounds on the global optimum, due to less overestimation in the interval computations, because some of the variables in the evaluation are fixed at their point boundary values.

Provided the <GlobSol root dir>directory is in the search path.

We have abridged the output to save space and for clarity. Lines that we have omitted consist mainly of echoing of configuration variables and of performance statistics; we have replaced groups of such lines with a single line consisting of ‘.’.

GlobSol does not allow this point to be too near to the boundary relative to the tolerance, if that boundary does not represent a bound constraint.

We hope to publicly release this version within a year of this report.

Other programs are available, as seen in <GlobSol root dir>/executables, but are not normally of interest as they do not add significant functionality than those listed in Table 1.

Also, because of the g95 compiler's handling of ‘\’ in output character strings, make_tex as distributed may work for the g95 versions, but not other versions.

With either constant objective or with objective equal to the sum of squares of the residuals, etc.

Finer control over the stopping tolerances can be obtained by adjusting particular variables in the GlobSol.CFG file. These tolerances are described in 11, and are documented in-line in GlobSol.CFG.

This means that redundant operations are removed.

Such as BOOST_license.txt and gnu_Fortran_95_and_gnu_make_license.txt.

For most builds.

GlobSol.a on Unix builds and on the build distributed for the g95 compiler, and GlobSol.lib on other MS-Windows builds.

The Fortran 2003 standardized interface to the c language may be useful in this context.

DAG stands for ‘Directed Acyclic Graph’, and is the internal representation of the objective and constraints within the COCONUT system.

Provided the COCONUT environment is installed and provided AMPL and GAMS are installed with appropriate licences.

But a need for matlab.

Defining this data type can be done by translating the GlobSol module CODELIST_CREATION in file <GlobSol root dir>/overload/overload.f90 into matlab syntax.

In an ‘m’ file.